128 Mr Rogers on the Construction of Achromatic Telescopes, 



in this construction limits the powers of the individuals com- 

 posing the correcting lenses, they may therefore be applied any 

 where that convenience may dictate ; and thus, theoretically 

 speaking, a disc of flint-glass, however small, may be made to 

 correct the colour of one of crown, however large. 



But this construction possesses other and very remarkable 

 advantages. For, first, when the correcting lens is approxi- 

 mately constructed on a calculation founded on its intended 

 aperture, and on the refractive and dispersive indices of its ma- 

 terials, the final and complete destruction of colour may be ef- 

 fected, not by altering the lenses by grinding them anew, but 

 by sliding the combination nearer to, or further from, the ob- 

 ject-glass, as occasion may require, along the tube of the tele- 

 scope by a screw motion, till the condition of achromaticity is 

 satisfied in the best manner possible. And, secondly, the sphe- 

 rical aberration may in like manner be finally corrected by 

 slightly separating the lenses of the correcting glass, whose sur- 

 faces should for this purpose be figured to curvatures, previ- 

 ously determined by calculation, to admit this mode of correc- 

 tion — a condition which the author finds to be always possible. 



Mr Rogers explains his construction by reference to a dia- 

 gram, and states the rule for the determination of the foci of 

 the lenses of the correcting glass in a formula which may be 

 thus interpreted :« — " The focal length of either lens of the cor- 

 recting lens is to that of the object-glass, in a ratio compound 

 of the ratio of the square of the aperture of the correcting lens 

 to that of the object-glass, and of the ratio of the differences of 

 the dispersive index of crown and flint-glass, to the dispersive 

 index of crown f — for example, to correct the colour of a lens 

 of crown or plate glass of nine inches aperture, and fourteen 

 feet focal length (the dimensions of the celebrated telescope of 

 Fraunhofer at Dorpat) by a disc of flint-glass three inches in 

 diameter, the focus of either lens of the correcting lens will re- 

 quire to be about nine inches. To correct it by a four inch 

 disc will require a focus of about sixteen inches for each. 



The author then remarks, that it is not indispensable to make 

 the correcting glass act as a plane lens. It is sufficient if it 

 be so adjusted as to have a shorter focus for red rays than for 

 violet. If, preserving this condition, it be made to act as a 



